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# Mixed number addition with regrouping

CCSS.Math:

## Video transcript

let's see if we can add five and two-fifths two three and four fifths pause this video and see if you can figure out what this is all right now let's do this together and we've got a little bit of practice adding mixed numbers in the past and so one way to think about it is you could view five and two fifths as five plus two fifths and then we're to that we're going to be adding three and four fifths which you could view as three plus four fifths and then you could just change the order with which you are adding and say all right well I could say five plus three so that's five plus three and then to that I could add two fifths and 4/5 so plus two fifths plus 4/5 and what is that going to get me well five plus three is going to be equal to eight eight plus and then if I have two fifths and I add four more fish to that well now I'm going to have six fifths two of something plus four of that something's gonna be six of that something and there's something in this case our fifths so now I'm going to have six fifths so some of you might be tempted to say hey isn't this just going to be equal to eight and six fifths and you wouldn't be completely wrong if you said that but pauses to do and think about why this feels a little bit off well the reason why this isn't standard is the fractional part of this mixed number six fifths is greater than one so there's a hole inside of this six fifths so the standard way to do this is see if we can break out that hole and what do i mean by that well I could rewrite eight plus six fifths as eight plus six fifths is the same thing as a hole or five fifths plus one-fifth and why is this useful well five fifths is the same thing as one and so now I can say this is going to be equal to 8 plus one whole is nine that's eight plus the five fifths and then what I have left over is one-fifth so nine and one-fifth and so though a direction that people will traditionally go in now there's another way that you could approach it which is really the same idea we're just writing things a little bit differently we could write this as five and two fists plus plus three and four fifths and notice the way that I wrote it I put all the fractions in the fraction column I guess you could call it that way and I put all of our whole numbers underneath each other and if I had multiple digits here I would align them according to place value and then what we could do is we could say okay two-fifths plus 4/5 is going to be six fifths we could write six fifths there but we say hey there's something a little bit fishy about six fifths that's really the same thing as five fifths plus one-fifth or you could say that's the same thing as 1 and 1/5 six fifths is equal to 1 and 1/5 and so what you could do is you could write the 1/5 part in the fractions column and then the 1 well now you're going to be regrouping that into our whole numbers so you put a 1 right over there notice 2/5 plus 4/5 is 1 and 1/5 what's the same thing as 6 bits and then you add the whole number parts 1 plus 5 plus 3 is 9 so you get 9 and 1/5 but hopefully you realize that these are really the same idea just different way of writing things